2-spanning cyclability problems of the some generalized Petersen graphs
Eddie Cheng, Lih‐Hsing Hsu, Chun‐Nan Hung, Meng‐Chien Yang · Discussiones Mathematicae Graph Theory · 2018
A graph G is called r-spanning cyclable if for every r distinct vertices v 1 , v 2 , . . . , v r of G, there exists r cycles C 1 , C 2 , . . . , C r in G such that v i is on C i for every i, and every vertex of G is on exactly one cycle C i . In this paper, we consider the 2-spanning cyclable problem for the generalized Petersen graph GP (n, k). We solved the problem for k 4. In addition, we provide an additional observation for general k as well as stating a conjecture.